gap> TestConjugacy := function(K, H, n)
> local G, P, i, g, h, c;
> G := WreathProduct(K, H);;
> P := WreathProduct(K, SymmetricGroup(MovedPoints(H)));
> for i in [1..n] do
> g := PseudoRandom(G);
> repeat
> h := g ^ PseudoRandom(P);
> until h in G;
> c := RepresentativeAction(G, g, h);
> if c <> fail and g ^ c <> h then
> return false;
> fi;
> od;
> return true;
> end;;
gap> K := SymmetricGroup(10);;
gap> H := DirectProduct([SymmetricGroup(5), SymmetricGroup(5)]);;
gap> TestConjugacy(K, H, 5);
true
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